The interaction potential between H and PsH, and between H and H- have been calculated using the diffusion Monte Carlo method. As far as the H-H- system is concerned, our results appear to be the most accurate published so far. The potential functions show the H-PsH system to be bound with respect to the H-2+Ps dissociation channel for nuclear distances larger than 3.5 bohr, while the H-2(-)-e(+) threshold lies 0.25 hartree above for all the distances studied. Moreover, the H-PsH potential curve presents a minimum located at 5.2 bohr that can be attributed to the van der Waals interaction between the two fragments. The relevancy of these results for the low energy scattering of Ps on H-2 and for the exchange reaction of H with Ps is discussed.